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Øving Plenum E&P Høst 2002 (HDA-prosess)

Norwegian University of Science and Technology Course: Energy and Process

Department of Energy and Process Engineering No.: TEP 4230

Trondheim, 17.09.04, T. Gundersen Part: Phys. and Chem. Equil.

Task: 6 Year: 2004 Assistance: 27.09 Deadline: 11.10

TOPIC: Thermodynamic Basis, the Phase Rule and Equations of State

Task 1: “Gibb’s Phase Rule”

a) Develop the Phase Rule on the basis of number of independent variables and number of equations in a PVT system consisting of m chemical components that distribute across  phases that are in equilibrium (the system is assumed to be non-reacting).

b) Show that the maximum number of co-existing phases in equilibrium is 3 for a PVT system consisting of only one chemical component.

Task 2: “Thermodynamic Functions”

a) Show that for a reversible and isothermal process in a closed PVT system, the work can be expressed by using the Helmholtz function: W = - dA

b) Show that for a reversible, isothermal and isobaric process in a closed PVT system, the work can be expressed in the following way: W = - dG + PdV

Task 3: “Van der Waal’s Equation of State”

One would like to find expressions for the two parameters (a) and (b) in Van der Waal’s cubic equation of state:

P = RT / (V – b) - a / V²

by using the following conditions that should apply at critical point:

( P / V ) _{T, Critical Point} = 0

( ²P / V² ) _{T, Critical Point} = 0

What is the compressibility in the critical point ?

Task 4: “Simple Models for K-values”

Develop a very simple model for K-values in gas/liquid equilibrium when we assume that Raoult’s law and Dalton’s law apply. Assume that an equation is available for calculating the vapor pressure for a chemical component as a function of temperature.

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